Answer to Question #157616 in Statistics and Probability for ssdfs

Question

The number of work-related injuries per month in a manufacturing plant is known to follow a Poisson distribution with a mean of 2.5 work-related injuries a month. What is the probability that in a given month no work-related injuries occur? What is the probability that atleast one work-related injury occurs

Answer 1

Let $X=$ the number of work-related injuries per month: $X\sim Po(\lambda).$

$$P(X=x)=\dfrac{e^{-\lambda}\cdot\lambda^x}{x!}$$

Given $\lambda=2.5$

$$P(X=0)=\dfrac{e^{-2.5}\cdot2.5^0}{0!}=e^{-2.5}\approx0.082085$$

$$P(X\geq1)=1-P(X=0)=1-e^{-2.5}$$

$$\approx0.917915$$